1. Field of the Invention
The present invention relates to projection optical system adjustment methods, prediction methods, evaluation methods, adjustment methods, exposure methods and exposure apparatus, programs, and device manufacturing methods, and more particularly to an adjustment method of a projection optical system that projects an image of a pattern on a first surface onto a second surface, a prediction method of characteristics of the image of the pattern via the projection optical system, an evaluation method for evaluating the characteristics of the image of the pattern that has undergone the prediction method, an adjustment method for adjusting the image of the pattern that has undergone the evaluation method, an exposure method in which a pattern is formed on an object using such adjustment method or (and) the adjustment method of the projection optical system and an exposure apparatus to which the exposure method or (and) the adjustment method of the projection optical system can suitably be applied, a program that makes a computer execute the prediction method, and a device manufacturing method that uses the exposure method or (and) the exposure apparatus.
2. Description of the Related Art
In general, in a lithographic process for manufacturing microdevices such as a semiconductor device, a display-device, a thin film magnetic head, and a micromachine, projection exposure apparatus such as the so-called stepper or the so-called scanner (also referred to as a scanning stepper) are used that transfer a pattern formed on a mask or a reticle (hereinafter generally referred to as a ‘reticle’) onto a photosensitive object such as a wafer or a glass plate (hereinafter generally referred to as a ‘wafer’) via a projection optical system.
Conventionally, with these kinds of exposure apparatus, when a line width difference is measured in a transferred image (such as a resist image) in between a vertical line pattern and a horizontal line pattern formed on a wafer by exposure, asymmetric aberration such as coma was considered the main cause for the contrast difference in the image of the vertical line pattern and the horizontal line pattern in the projection optical system. Therefore, when the measurement found that asymmetric aberration such as coma could not be measured, correction of the line width difference was difficult.
In recent years, when the projection optical system is being assembled, adjustment is performed where wavefront aberration at each point within the field of the projection optical system (or the exposure field) is measured using an interferometer, the wavefront aberration measured (aberration function) is expanded into series using the Zernike polynomial (for example, the Fringe Zernike polynomial), and each coefficient (Zernike coefficient) of each term (each Zernike term) in the series obtained is adjusted so that it does not exceed its target value. The reason for performing such an adjustment is because each term of the series (each Zernike term) represents a specific wavefront aberration component, and the coefficient of each term shows the magnitude of each aberration component.
Recently, the control accuracy of the aberration of the projection optical system (projection lens) has significantly improved, due to introducing the above wavefront measurement into the making process of the projection optical system, and the control by series expansion that uses the Zernike polynomial of the wavefront aberration.
In addition, the influence of simple aberration can also be judged by a simple method, by the so-called Zernike sensitivity method for obtaining image forming qualities such as aberration (or its index value) of the projection optical system, based on a linear combination of the magnitude (Zernike coefficient) of each term (each Zernike term), which is obtained expanding the wavefront aberration (aberration function) using the Zernike polynomial, and a Zernike Sensitivity table. In this case, the Zernike Sensitivity table refers to a calculation table made up of: different exposure conditions, that is, optical conditions (such as exposure wavelength, maximum N. A., N.A. in use, illumination N.A., and the aperture shape of the illumination system aperture stop); evaluation items (such as mask type, line width, evaluation amount, and information on the pattern); and a variation amount of the image forming qualities of the projection optical system obtained under a plurality of exposure conditions that are decided by a combination of such optical conditions and evaluation items, for example, the variation amount per 1λ of each Zernike term of various aberrations (or their index values).
When it comes to evaluating line width variation, however, the so-called Zernike sensitivity method is not necessarily suitable. Regarding the line width variation, as it is disclosed in Proc. SPIE Vol. 4346 on page 713, the focus position where the line width is the widest shifts according to a O-times rotational symmetry component (0θ component) and a 2-times rotational symmetry component (2θ component) of an aberration, and the maximum value of the line width also changes. Furthermore, interaction occurs between the two aberrations (the 0θ component and the 2θ component). For such reasons, the so-called Zernike sensitivity method has not been applied when estimating the line width.
The rotational symmetry component (0θ component) terms described above expanding the wavefront aberration in series using the Fringe Zernike polynomial, include low order terms that represents defocus, that is, the fourth term (coefficient Z4), and the ninth term (coefficient Z9), which represents low order spherical aberration, and the shift of wavefront by such 0θ component terms is isotropic, therefore, the influence on the image forming state of the V-line (vertical line) and H-line (horizontal line) patterns is identical. In addition, the 2-times rotational symmetry component (2θ component) terms include the fifth term (coefficient Z5), which represents astigmatism in low order, and the twelfth term (coefficient Z12), which represents astigmatism in high order, and such 2θ component terms affect the image forming state of the vertical line pattern and the horizontal line pattern so that they are opposite in sign while being equal in magnitude. Therefore, conventionally, the difference that the influence of aberration has on the pattern images of the vertical and horizontal lines due to both the 0θ component terms and 2θ component terms being available (that is, the coefficients (components) of both terms are not zero) was not considered.
Due to such circumstances, in the present state of affairs, there is no simple and solid judgment method regarding the line width difference of the images of the vertical line pattern and the horizontal line pattern, therefore, its adjustment is also difficult.